{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from matplotlib import pyplot as plt\n",
    "from efficient_kan import KANLinear\n",
    "layer = KANLinear(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000],\n",
      "        [-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000],\n",
      "        [-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000],\n",
      "        ...,\n",
      "        [-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000],\n",
      "        [-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000],\n",
      "        [-2.2000, -1.8000, -1.4000,  ...,  1.4000,  1.8000,  2.2000]])\n",
      "tensor(0.6631)\n"
     ]
    }
   ],
   "source": [
    "# get b-spline basis (thx to efficient_kan)\n",
    "x = torch.linspace(-3, 3, 100)\n",
    "basis = layer.b_splines(x[None])\n",
    "print(layer.grid)\n",
    "print(basis[0, :, 0].max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([100, 8])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate radial basis functions with gaussian density kernel\n",
    "def rbf(x, grid, h):\n",
    "    return torch.exp(-((x[..., None] - grid) / h)  ** 2 )\n",
    "rbf_basis = rbf(x, torch.linspace(-1.4, 1.4, 8), .33)\n",
    "rbf_basis.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 5))\n",
    "ax = fig.subplots(1, 1)\n",
    "for i in range(8):\n",
    "    rbf_plt = ax.plot(x.numpy(), rbf_basis[:, i].numpy() * .6631, color=\"red\", label=None if i > 0 else \"Gaussian RBF basis\")\n",
    "    bspline_plt = ax.plot(x.numpy(), basis[0, :, i].numpy(), \"--\", color=\"blue\", label=None if i > 0 else \"3-order B-spline basis\")\n",
    "ax.legend()\n",
    "fig.savefig(\"img/compare_basis.png\", dpi=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conclusion: Gaussian Radial Basis Functions can well approximate 3-order B-Spline basis with linear scalings."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
